Estimating gravimetric effects for ordinary bodies

TL;DR

This paper explores the proportionality of mass and weight for ordinary bodies, analyzing small gravimetric effects related to internal geometry to improve educational explanations.

Contribution

It introduces a detailed analysis of second-order gravimetric effects linked to internal geometry, offering a more precise understanding for teaching purposes.

Findings

Gravimetric effects are extremely small but measurable.

Internal geometry influences weight measurements.

The approach enhances educational demonstrations of mass-weight proportionality.

Abstract

The main topic of this article is a discussion about the best way to show students that the proportionality of mass and weight, strictly true for point-like particles, is an excellent approximation for objects of "normal" size. The usual way of addressing this issue, although very simple, is not entirely satisfactory. Our approach considers first and second order, coordinate dependent, gravimetric effects, connected to the internal geometry of objects; these effects, extremely small, are estimated through examples.